Integrated circuit “dies” or “dice” are small cubes of semiconductor material such as silicon that have various interconnected electrical circuits formed therein. Each die typically has a metalized surface layer with electrical contact regions thereon that allows the die to be connected to other electronic components. Integrated circuit dice are produced by “singulating” (“dicing”) a unitary semiconductor wafer having identical circuits formed in adjacent regions thereof that are arranged in a rectangular generally waffle-shaped grid. Saw cuts or laser fractures are made along “saw streets” to cut the wafer into dice. A diced wafer is often supported on a deformable sheet known as dicing tape. The dicing tape may be stretched by force applied to its outer perimeter. Stretching the dicing tape causes the diced wafer supported on it to expand laterally, thereby separating the dice. The separated dice may then be picked up, one at a time, by pick and place machines or the like. With very small dice, i.e., less than about 1.0 mm, current methods of expanding the dicing tape tend to provide insufficient space between dice, or the space provided shrinks sufficiently after initial expansion, such that handling of the dice is difficult and often ends with damage to adjacent dice.